Irregular sampling restoration. Theory and applications to satellite images and signals.
Performances of remote-sensing satellite instruments have been increasing fast thanks to developing technologies but also thanks to the better understanding and integration of complicated physical phenomena occurring during the acquisition. This thesis report addresses several irregular sampling problems including the microvibrations of push-broom satellites such as SPOT5 and recently launched Pleiades satellites whose imaging capabilities allow for the computation of very accurate numerical elevation models. We also address the inversion of interferograms in spectrogrametry where the sampling irregularity comes from the imperfectly machined reflecting components. Microvibrations in the single pitch case are estimated from a perturbed, non-dense disparity map with sparsity constraints. Experiments show that this modelling and the developed algorithms enable partial resolution of this ill-posed problem. Furthermore, an additional regularity hypothesis on the elevation improves this estimation for more di cult cases. Images suffering from microvibrations during acquisition necessitate a sampling correction together with deblurring and fast restoration. The algorithm we present here fulfills these requirements thanks to an adaptation of the splines setting to the deblurring case, it is faster than state-of-the-art algorithms with equivalent performances. Finally we address the interferogram inversion problem in which the signals and sampling sets raise many questions, this work was achieved during a R&T study of the SIFTI instrument examined at CNES, it clarifies these questions in the form of theoretical and numerical results using the unifying framework of nonharmonic Fourier series.